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lfunc_lfunctions • Show schema
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{'Lhash': '3531289055113180675651004625643', 'a10': [-11.771942770419233, 6.823253626748955e-61], 'a2': [-1.0, -1.7320508075688772], 'a3': [3.4232328456792174, -5.929213214854995], 'a4': [-2.0, 3.4641016151377544], 'a5': [2.9429856926048084, -5.097400745539811], 'a6': [-13.69293138271687, 6.176307070676117e-61], 'a7': [8.40191907560336, -14.552550720027153], 'a8': [8.0, 0.0], 'a9': [-9.937046231474067, -17.21146895007393], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.366141340424807, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.7320508075688772]]], [37, [[1.0, 0], [131.38018872823832, -182.73545362006925]]]], 'bad_primes': [2, 37], 'central_character': '74.63', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '1421062390802375319133062180306', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.7320508075688772]], [[1.0, 0], [-3.4232328456792174, 5.929213214854995], 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[805.2440824765548, 1394.7236633435764], [-721448.5, 1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-74-37.26-c3-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/74/4/c/b/63/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4923591179181914, 1.6512405203289944, 1.8065824204406227, 1.9573951125018865, 2.102204104711187, 2.238974027621371, 2.3650704461904057, 2.4772633114628473, 2.5717744066694816, 2.6443699540606085, 2.6904984139106656, 2.7054722236855606, 2.684690603703404, 2.623898476136342, 2.5194739869890737, 2.368734170904545, 2.170245136472523, 1.9241200328699515, 1.6322853018720933, 1.298693671941403, 0.9294613726037875, 0.5329074790946229, 0.11947543140351087, -0.29847918292507924, -0.7070444460699656, 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'9.953248874927150888429393778197052', '10.58762441944922802796684056639430', '12.30626394186391392501721427042820', '13.95894918866992435310021523918701', '14.72346269683659497459229199884060'], 'prelabel': '2-74-37.26-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0895313686146966, 'root_angle': 0.7452394575805806, 'root_number': '-0.6964528303664479 + 0.7176025746014041*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.37261972879', 'prec': 44}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.78569588061363515472380408982', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.67654268088849477023687186482', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.97162332133673193887359805850', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.366141340424807, 'bad_primes': [2, 37], 'central_character': '37.26', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/4/c/b/63/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-74-37.26-c3-0-8', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-74-37.26-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0895313686146966, 'root_angle': 0.3726197287902903, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.78569588061363515472380408982', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3531289055113180675651004625643', 'Lhash_array': ['3531289055113180675651004625643'], 'label': '2-74-37.26-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/4/c/b/63/5'}